On a mixed problem for the parabolic Lamé type operator
URI (for links/citations):https://elib.sfu-kras.ru/handle/2311/28049
Институт математики и фундаментальной информатики
Кафедра теории функций
Journal Name:Journal of Inverse and Ill-Posed Problems
Journal Quartile in Scopus:Q3
Journal Quartile in Web of Science:Q1
Bibliographic Citation:Puzyrev, Roman. On a mixed problem for the parabolic Lamé type operator [Текст] / Roman Puzyrev, Alexander Shlapunov // Journal of Inverse and Ill-Posed Problems. — 2015. — Т. 23 (№ 6). — С. 555-570
We consider a boundary value problem for a Lam e type operator, which corresponds to a linearisation of the Navier-Stokes' equations for compressible ow of Newtonian uids in the case where pressure is known. It consists of recovering a vector function, satisfying the parabolic Lam e type system in a cylindrical domain, via its values and the values of the boundary stress tensor on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding H older spaces; besides, additional initial data do not turn the problem to a well-posed one. Using the integral representation's method we obtain a uniqueness theorem and solvability conditions for the problem. We also describe conditions, providing dense solvabilty of the problem.
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